Quantum computing and the internet

Not all the internet technologies will be vulnerable to quantum computing.

Quantum computing is very fast at particular types of calculations, but otherwise is in the same league as regular present computing in others. When it comes to cryptography on the web, it depends on the where it is used as to how much it can do some tasks more quickly. It is important to start with adequate bits of information that trying to guess, by quantum or conventional, is computationally not worth trying.

Keys, preferably 256bit, used for symmetric cryptography are shared, and even with Grover's algorithm effectively halving that, they are still extremely safe. Applications involving multiple technologies, like AES-GCM, are dependent upon TLS, each version of which is configured to negotiate handshaking over particular protocols, some of which in versions prior to 1.3 are quantum vulnerable.

So while the actual traffic over the internet may be safe, it is the public key infrastructure-based handshake setup that is most quantum-vulnerable. Those vulnerable protocols and technologies are being investigated and upgraded now so that data encrypted before the several years before viable stable quantum computers are available will not be able to be decrypted then.